Physical waves contain information about the physical properties of the objects which emit or reflect them. Measuring and analyzing the waves emitted or reflected by an object of interest is therefore a common technique to gather information about the object. The analysis of emitted or reflected waves can reveal aspects of the object's external geometry, its internal structure, its chemical composition, or its state of motion. Acoustic and electromagnetic waves are most commonly used for this purpose, but many principles used to interpret the properties of received waves are independent of the physical nature of the waves and can hence be generalized to different modalities.
Example applications which analyze received physical waves include sonar (sound waves, most often in water), radar (electromagnetic waves, in air or in space), biomedical ultrasound as well as other modalities used in biomedical diagnosis, and non-destructive testing (e.g., ultrasonic waves in solids).
All sample applications given above make frequent use of sensor arrays. Sensor arrays measure wave-fields at a set of different points in space concurrently. Array output can be used to estimate the spatial characteristics of the wave-field. From these spatial characteristics, both, deterministic and statistical average properties of a wave-source or -reflector can be deduced.
The sensor positions within an array are commonly arranged in a regular fashion, for example in a plane or along some other simple line or surface geometry. The arrangement of the sensors defines the spatial resolution of the array. A high spatial resolution, i.e., many sensors per distance or area unit is favorable for many applications of array sensors because it allows for the analysis of wave-field properties with high spatial frequencies. The maximum number of sensors in an array is limited by the overall size of the array and the size of the individual sensors. The overall size of the array is constrained by the context of the application and the manufacturing cost. The minimum size of the individual sensors is limited by their sensitivity and hence the signal-to-noise ratio of their output signals, both of which typically decrease with sensor size. Together, these two limitations make high array resolutions difficult to achieve.
For high-frequency signals, handling the output of the array can be impractical because of the bandwidth requirements imposed on subsequent signal processing elements cannot be met with reasonable effort. The method of envelope detection is often employed as a remedy in cases where the centered bandwidth of a signal is significantly smaller than its center frequency. In envelope detection, the signal is subjected to an amplitude-demodulation. A person having ordinary skill in the art will know of ways to conveniently approximate envelope detection by such simple operations as, for example, a rectification combined with subsequent lowpass filtering.
A signal processing operation frequently used to extract useful information from the spatial characteristics of a wave-field is spatial bandpass filtering. In spatial bandpass filtering as implemented in prior art, the signals received as a function of sensor position in the array at the same instant in time are treated as a series of input values to the filters. This operation is capable of separating spatial properties existing on various size scales, because output signal components relating to these properties are found in different bandpass channels: Wave-field components varying slowly in space give rise to signals only in bandpass channels with low center- and lower-edge cut-off frequencies, whereas components which exhibit fast spatial changes are detected in bandpass channels with high center and upper-edge cutoff frequencies. Abrupt changes in the wave-field properties over spatial position give rise to a broadband component in the spatial array output. Such a broadband component can be detected by virtue of its simultaneous occurrence in several bandpass channels with non-identical or even non-overlapping passbands. Detection of such abrupt changes is informative, because these signal components correspond to spatial discontinuities in the wave-emitting or reflecting properties, i.e., borderlines at which an object ends or along which its properties change. Because of the nature of wave propagation in which contributions from any emitting or reflecting point can—potentially—impact any sensor, “edges” seen in an array output signal may also reflect spatially distributed properties of the reflector or emitter. Besides their application in interpreting an array output signal, bandpass filters are also commonly used for compressing signals and reducing the transmission bandwidth required by a signal. The decomposition of a signal into a set signals which reflect information at different scales is commonly referred to as a “multiresolution” pyramid in the areas of image processing and pattern recognition. Here, the term “multiresoltion decomposition” is used to denote such a decomposition regardless of the physical nature of the signal, its origin, its dimensionality, or the intended use of the representation.
In image processing and image analysis, the concepts of spatial bandpass filtering and detection of spatial discontinuities are formalized by the notion of multiresolution decompositions using a set of wavelets as orthogonal basis functions. These concepts are used extensively in algorithms for image representation and compression as well as for the purpose of image interpretation. For the latter objective, spatial bandpass filter impulse responses such as the Laplacian of Gaussian (“Mexican Hat”) and the Difference of Gaussian functions have been used extensively to detect edges which are particularly informative about image content.
The far-field behavior of an individual sensor for a wave is described completely by its directivity pattern. The directivity pattern specifies how the sensor's sensitivity is distributed as a function of direction and frequency. Therefore, the directivity pattern is also a description of a spatial filtering operation performed by the individual sensor.